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Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°

Find: CD

2 Answers

5 votes

Answer:

9.92 cm

Explanation:

Using Trig functions, we can calculate the lengths.

User Apotek
by
7.2k points
3 votes

Answer:

9.92 cm

Explanation:

Given: ∆ABC,

CD ⊥ AB,

AC = BC,

Area of ABC = 32 cm2,

m∠A = 72°

Find: CD

Solution:

Triangle ABC is isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,


m\angle A=m\angle B=72^(\circ)

The sum of the measures of all interior angles is 180°, thus


m\angle C=180^(\circ)-m\angle A-m\angle B\\ \\m\angle C=180^(\circ)-72^(\circ)-72^(\circ)=36^(\circ)

The area of the triangle ABC is


A_(ABC)=(1)/(2)AC\cdot BC\cdot \sin \angle C\\ \\32=(1)/(2)AC^2\sin 36^(\circ)\\ \\AC^2=(64)/(\sin 36^(\circ))\\ \\AC\approx 10.43\ cm

Consider right triangle ACD. In this triangle,


\sin \angle A=(CD)/(AC)\\ \\\sin 72^(\circ)=(CD)/(10.43)\\ \\CD=10.43\sin 72^(\circ)\approx 9.92\ cm

Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72° Find: CD-example-1
User Dave Riedl
by
6.6k points